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Theorem ltrel 9437
Description: 'Less than' is a relation. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ltrel  |-  Rel  <

Proof of Theorem ltrel
StepHypRef Expression
1 ltrelxr 9436 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4945 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4925 . 2  |-  (  <  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <  ) )
41, 2, 3mp2 9 1  |-  Rel  <
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3326    X. cxp 4836   Rel wrel 4843   RR*cxr 9415    < clt 9416
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-v 2972  df-un 3331  df-in 3333  df-ss 3340  df-pr 3878  df-opab 4349  df-xp 4844  df-rel 4845  df-xr 9420  df-ltxr 9421
This theorem is referenced by:  dflt2  11123  gtiso  25994  ballotlemimin  26886
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